Guest lectures on five subjects viz., Economics, History, Statistics, English and Mathematics have to be arranged in a week from Monday to Friday. Only one lecture can be arranged on each day. Economics cannot be scheduled on Tuesday. Guest faculty for History is available only on Tuesday. Mathematics lecture has to be scheduled immediately after the day of Economics lecture. English lecture has to be scheduled immediately before the day of Economics lecture.
Which lecture is the last one in the week?

Correct Option (3)

The schedule for the guest lectures can be determined by systematically applying the given constraints:

• The constraint "Guest faculty for History is available only on Tuesday" directly establishes that History must be scheduled on Tuesday.
• The conditions "Mathematics lecture has to be scheduled immediately after the day of Economics lecture" and "English lecture has to be scheduled immediately before the day of Economics lecture" imply a fixed sequence of three lectures: English - Economics - Mathematics. This block requires three consecutive days.
• Considering that Tuesday is occupied by History, the only remaining block of three consecutive days in the week (Monday to Friday) is Wednesday, Thursday, Friday.
• Therefore, the English - Economics - Mathematics block must be scheduled as:
  • Wednesday: English
  • Thursday: Economics
  • Friday: Mathematics
• This arrangement also satisfies the condition that Economics cannot be scheduled on Tuesday.
• With History on Tuesday and the English-Economics-Mathematics sequence occupying Wednesday, Thursday, and Friday, the only remaining day is Monday and the only remaining subject is Statistics. Thus, Statistics is scheduled on Monday.

The complete schedule is:

• Monday: Statistics
• Tuesday: History
• Wednesday: English
• Thursday: Economics
• Friday: Mathematics

Based on this schedule, Mathematics is the last lecture in the week, scheduled on Friday.

Incorrect Options:

• History: History is scheduled on Tuesday, as per the explicit availability constraint, making it an early lecture in the week, not the last.

• English: English is scheduled on Wednesday, immediately preceding Economics, and thus cannot be the last lecture.

• Economics: Economics is scheduled on Thursday, between English and Mathematics, and therefore is not the last lecture of the week.